Prospect theory-based large-scale group decision-making method with heterogeneous preference relations

Large-scale group decision-making (LSGDM) issues are increasingly prevalent in modern society across various domains. The preference information has emerged as a widely adopted approach to tackle LSGDM problems. However, a significant challenge lies in facilitating consensus among decision-makers (DMs) with diverse backgrounds while considering their hesitation and psychological behavior. Consequently, there is a pressing need to establish a novel model that enables DMs to evaluate alternatives with heterogeneous preference relations (HPRs). To this end, this research presents a new consensus-building method to address LSGDM problems with HPRs. First, a novel approach for solving collective priority weight is introduced based on cosine similarity and prospect theory. In particular, a new cosine similarity measure is defined for HPRs. Subsequently, a consensus index is provided to gauge the consensus level among DMs by considering their psychological behavior and risk attitudes. Further, a consensus-reaching model is developed to address LSGDM with HPRs. Finally, an instance of supplier selection is presented to demonstrate the practicality and efficacy of the proposed method.